How to catch a lion in the Sahara Desert

The Hilbert, or axiomatic method:

We place a locked cage at a given point of the desert. We then
introduce the following logical system:Axiom 1. The class of lions in the Sahara Desert is non-voidAxiom 2. If there is a lion in the Sahara Desert, there is a lion
in the cage.Rule of Procedure. If p is a theorem, and p implies q
is a theorem, then q is a theorem.Theorem 1. There is a lion in the cage

The Method of Inversive Geometry:

We place a spherical cage in the desert, enter it, and lock it. We
perform an inverse operation with respect to the cage. The lion is
then in the interior of the cage and we are outside.

The Method of Projective Geometry:

Without loss of generality, we may regard the Sahara Desert as a
plane. Project the plane into a line, and then project the line into
an interior point of the plane. The lion is projected into the same
point.

The Bolzano-Weirstrauss Method

Bisect the desert by a line runing N-S. The lion is either in the E
portion or in the W portion; let us suppose him to be in the W
portion. Bisect this portion by a line running E-W. The lion is either
in the N portion or in the S portion; let us suppose him to be in the
N portion. We continue this process indefinitely, constructing a
sufficiently strong fence about the chosen portion at each step. The
diameter of the chosen portions approaches zero, so that the lion is
ultimately surrounded by a fence of arbitrarily small perimeter.

The `Mengentheorisch' method

We observe that the desert is a separable space. It therefore contains
an enumerable dense set of points, from which can be extracted a
sequences having the lion as limit. We then approach the lion
stealthily along this sequence, bearing with us suitable equipment.

The Peano Method

Construct, by standard methods, a continuous curve passing through
every point of the desert. It has been remarked [1] that it is
possible to traverse such a curve in an arbitrarily short time. Armed
with a spear, we traverse the curve in a time shorter than that in
which the lion can move his own length.

Topological Method

We observe that the lion has at least the connectivity of the
torus. We transport the desert into four-space. It is then possible
[2] to carry out such a deformation that the lion can be
returned to three-space in a knotted condition. He is then helpless.

The Cauchy, or function theoretical, Method

We consider an analytic lion-valued function f(z). Let X be the cage.
Consider the integral:

1/(2 * pi * i) integral over C of [f(z) / (z - X)]dz

where C is the boundary of the desert; its value is f(X), i.e., a
lion in the cage.

The Dirac Method

We observe that wild lions are ipso facto not observable in the Sahara
desert. Consequently, if there are any lions in the Sahara, then they
are tame. The capture of a tame lion is left as an exercise for the
reader.

The Thermodynamic Method

We construct a semi-permeable membrane which is permeable to
everything except lions and sweep it across the desert.

The Wiener Tauberian method

We procure a tame lion, L0 of class
L(-infinity, +infinity), whose Fourier transform nowhere vanishes, and
release it in the desert. L0 then
converges to our cage. By Wiener's General Tauberian Theorem, any
other lion, L (say), will then converge to the same cage.
Alternatively, we can approximate arbitrarily closely to L by
translating L0 about the desert.

The Schrödinger Method

At any given moment there is a positive probability that there is a
lion in the cage. Sit down and wait.

The Heisenberg Method

You will disturb the lion when you observe it before capturing. So
keep your eyes closed.

The Einstein Method

Run in the direction opposite to that of the lion. The relative
velocity makes the lion run faster and hence it feels heavier and gets
tired.

Another Einstein Method

We distribute about the desert lion bait containing large portions of
the Companion of Sirius. When enough bait has been taken, we project
a beam of light across the desert. This will bend right around the
lion, who will then become so dizzy that he can be approached with
impunity.

The Magneto-Optical Method

We plant a large lenticular bed of catnip [Nepeta cataria],
whose axis lies along the direction of the horizontal component as the
earth's magnetic field, and place a cage at one of its foci. We
distribute over the desert large quantities of magnetized spinach
[Spinacia oleracea], which, as is well known, has a high
ferric content. The spinach is eaten by the herbivorous denizens of
the desert, which are in turn eaten by lions. the lions are then
oriented parallel to the earth's magnetic field, and the resulting
beam of lions is focused by the catnip upon the cage.

Contributions from Computer Science

1 The search method

We assume that the lion is most likely to be found in the direction to
the north of the point where we are standing. Therefore the REAL
problem we have is that of speed, since we are only using a PC to
solve the problem.

2 The parallel search method

By using parallelism we will be able to search in the direction to the
north much faster than earlier.

3 The Monte-Carlo method

We pick a random number indexing the space we search. By excluding
neighboring points in the search, we can drastically reduce the number
of points we need to consider. The lion will according to probability
appear sooner or later.

4 The practical approach

We see a rabbit very close to us. Since it is already dead, it is
particularly easy to catch. We therefore catch it and call it a lion.

5 The common language approach.

If only everyone used ADA/Common Lisp/Prolog, this problem would be
trivial to solve.

6 The standard approach

We know what a Lion is from ISO 4711/X.123. Since CCITT have specified
a Lion to be a particular option of a cat we will have to wait for a
harmonized standard to appear. $20,000,000 have been funded for
initial investigastions into this standard development.

7 Linear search

Stand in the top left hand corner of the Sahara Desert. Take one step
east. Repeat until you have found the lion, or you reach the right
hand edge. If you reach the right hand edge, take one step
southwards, and proceed towards the left hand edge. When you finally
reach the lion, put it the cage. If the lion should happen to eat you
before you manage to get it in the cage, press the reset button, and
try again.

8 The Dijkstra approach

The way the problem reached me was: catch a wild lion in the Sahara
Desert. Another way of stating the problem is: